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Proof step 2 from proof band-31-pos (previous step)

i < 32, 0 ≤ i ⊦ band(i, 31) = i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 ≤ j ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i → band(j, i) = j % (i + 1)
Proof step 4:
¬(0 ≤ i ∧ ¬ false ∈ int2bits(31).rest ∧ 0 ≤ 31), i < 32, 0 ≤ i ⊦ band(i, 31) = i

Rule argument

name: band-011x-pos-02 rotate: F subst: [i, j] → [31, i]

Additional information

Used simplifier rules: 0 < j ⊦ 0 ≤ i ∧ i < j → i % (* j) = i; Used terms: 31, i